[R] question: mediation results are not in line with compression of glmm consisted models

[Uri Blasbalg]

hi all,
I'll begin with my two question and all the related information
(description of the research and the data and full output) will follow.

1. When i execute model1 (glmm with random intercept only for subjects):
predictor (suppBin) and outcome (DtlsBinUp) and pre-intervention variables,
it results with significance . when I carry out model 2: add the mediator
(rlctDown) too as a predictor, the association shown in the model1 isn't
significant anymore (suppBin-DtlsBinup), and for the mediator and outcome
it is (rlctDown-dtlsBinup), with higher coefficient. that should imply for
full mediation, meaning there isn't direct effect between the predictor and
the outcome, only indirect. but when i the test mediation model (monte
carlo method), I gel significant effect for total effect, direct effect and
the indirect effect. how can it be that the monte carlo contradicts what
shown when substracting model1 from model2? what am i missing?

2.i am having trouble in interpreting the values of the effects estimations
in the monte carlo test. I understood the coefficients for the glmm
as log odds that after transforming using exponential function can be
understood as odds and may also be expressed as probabilities. but
the estimates in the monte carlo output are much lower than those in the
glmm output. so how should they be understood.

following are description and output,
thank you
uri.





********** predictor - outcome


Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: dtlsBinUp ~ suppBin * qu + ageS + gender + (1 | PD)
   Data: hypoTest
Control: glmerControl(tolPwrss = 0.001)

     AIC      BIC   logLik deviance df.resid
 15351.9  15406.1  -7669.0  15337.9    17111

Scaled residuals:
    Min      1Q  Median      3Q     Max
-0.6655 -0.5281 -0.5140 -0.1889  5.4472

Random effects:
 Groups Name        Variance Std.Dev.
 PD     (Intercept) 0        0
Number of obs: 17118, groups:  PD, 200

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) -3.20574    0.14668 -21.856  < 2e-16 ***
suppBin      0.57468    0.15930   3.607 0.000309 ***
qu           2.02646    0.10902  18.588  < 2e-16 ***
ageS        -0.09564    0.09923  -0.964 0.335151
gender      -0.05598    0.04141  -1.352 0.176458
suppBin:qu  -0.15165    0.17283  -0.877 0.380250
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
           (Intr) suppBn qu     ageS   gender
suppBin    -0.495
qu         -0.718  0.655
ageS       -0.673  0.010  0.002
gender     -0.179  0.008  0.034  0.065
suppBin:qu  0.456 -0.922 -0.631 -0.004 -0.028



********** predictor, mediator - outcome


Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: dtlsBinUp ~ suppBin * qu + rlctDown + ageS + gender + (1 | PD)
   Data: hypoTest
Control: glmerControl(tolPwrss = 0.001)

     AIC      BIC   logLik deviance df.resid
 14114.1  14176.0  -7049.0  14098.1    17110

Scaled residuals:
    Min      1Q  Median      3Q     Max
-1.5239 -0.4638 -0.4552 -0.1487  6.8990

Random effects:
 Groups Name        Variance Std.Dev.
 PD     (Intercept) 0        0
Number of obs: 17118, groups:  PD, 200

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) -3.69635    0.15247  -24.24   <2e-16 ***
suppBin      0.14896    0.16475    0.90    0.366
qu           2.26040    0.11289   20.02   <2e-16 ***
rlctDown     2.06709    0.05947   34.76   <2e-16 ***
ageS        -0.10680    0.10432   -1.02    0.306
gender      -0.02293    0.04360   -0.53    0.599
suppBin:qu   0.13720    0.17963    0.76    0.445
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
           (Intr) suppBn qu     rlctDw ageS   gender
suppBin    -0.462
qu         -0.708  0.629
rlctDown   -0.159 -0.088  0.143
ageS       -0.665  0.000 -0.018 -0.005
gender     -0.184  0.008  0.035  0.024  0.066
suppBin:qu  0.426 -0.916 -0.607  0.062  0.005 -0.029




********** predictor, mediator - outcome (function "mediate" from packege
"mediation"

** script (syntax):
med.out.8.1.2.1 <- mediate(model3.1, model8.1.2.med, treat = "suppBin",
mediator = "rlctDown",
                   sims = 1000)


Causal Mediation Analysis

Quasi-Bayesian Confidence Intervals

Mediator Groups: PD

Outcome Groups: PD

Output Based on Overall Averages Across Groups

                         Estimate 95% CI Lower 95% CI Upper p-value
ACME (control)             0.0401       0.0321       0.0481       0
ACME (treated)             0.0420       0.0338       0.0506       0
ADE (control)              0.0376       0.0178       0.0575       0
ADE (treated)              0.0395       0.0189       0.0595       0
Total Effect               0.0796       0.0580       0.1013       0
Prop. Mediated (control)   0.5015       0.3890       0.6852       0
Prop. Mediated (treated)   0.5276       0.4127       0.7081       0
ACME (average)             0.0410       0.0329       0.0492       0
ADE (average)              0.0385       0.0183       0.0584       0
Prop. Mediated (average)   0.5145       0.3999       0.6961       0

Sample Size Used: 17118


Simulations: 1000

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